I have 100 (one hundred) bottles of visually identical water, exactly one of which is poisonous. In this experiment, the only test I can do is to let some mice drink it. If a mouse drinks the poisonous water, it will die after a day.

Had the question given me only 1 day, I would have directly and immediately answered $7$, as it's obvious that

$$ 2^6 = 64 \lt 100 \le 128 = 2^7$$

The actual question is a single-choice quiz that reads

You have 100 bottles of water that look identical. One of them is poisonous. You can have mice drink them. If a mouse dies after one day, you know the water is poisonous. Now you have $2$ days to do the experiment. What is the minimum number of mice you need to find out which water is poisonous?

The four options available are $3,4,5,6$, so "2 days" must means "2 passes", which indicates that mice that remain alive after the first day can be used in the second day.

What's the answer?

Note: I don't know the answer, so it'd be good if you can prove the number is the smallest possible. FWIW, it's not hard to figure out a solution using 6 mice.



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